Week of April 10, 2017

Welcome back from spring break!

Tutoring: See me for times as schedule is not set for the week

Assessments: Test is likely on Friday

Monday
Welcome back from break! Today, we look at your heartrate and the medicine problem.
Help: ( not much on the web here)
HW;  None

Tuesday
Today, we look at the building problem and the TV problem.
Help:http://www.metric-conversions.org/length/feet-to-meters.htm
HW; None

Wednesday
It is TV problem day two.
Help:https://www.quora.com/How-does-one-calculate-a-televisions-height-and-width-based-on-its-diagonal-length-and-aspect-ratio
HW; None

Thursday
Review day!
Help:http://www.metric-conversions.org/
HW; Study for test

Friday
Test day!
HW; None

Have a great weekend!
Ms. Harrell

Week of 04.10.2017-04.14.2017 Algebra 2

Tutoring: Tuesday afternoon

Assessments: Unit test is Friday

Monday
Welcome back from break! Today, we  look at add and subtract rational expressions
Help:http://www.mesacc.edu/~scotz47781/mat120/notes/rational/add_subtract/add_subtract.html
HW; None


Tuesday
It is rational equations today
Help:http://www.purplemath.com/modules/solvrtnl.htm
HW; None


Wednesday
It is rational equations day two  today, be ready to find the LCD of all 3 denominators and applications.
Help:https://www.youtube.com/watch?v=Y6x06SBbEcA
HW; None


Thursday
It is  application wrap up and review day.
Help:https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/modeling-with-rational-functions/v/applying-rational-equations-1
HW; None


Friday
Test day!
Help:http://tutorial.math.lamar.edu/Classes/Alg/RationalExpressions.aspx

HW; None


Algebra 1

Transform means change, and these transformations change the simple quadratic $y=x^2$y=x2 into other quadratics by moving (translations), flipping (reflecting) and making the graph appear more or less steep (dilating).

By using the above applet, step through these instructions.

• Start with the simple quadratic $y=x^2$y=x2
• Dilate the quadratic by factor of $2$2.
• Reflect on the $x$x axis
• Translate vertically by $2$2 and horizontally by $-3$−3 units.  

How has the graph changed? Can you visualize the changes without using the applet?  What is the resulting equation?

Equations and Transformations of Quadratics

Transformations of quadratics will change the equation of the quadratic.  Here are some of the most common types of quadratic equations, and what they mean with regards to the transformations that have occurred.  

$y=ax^2$y=ax2

 If $a<0$a<0 (that is $a$a is negative) then we have a reflection parallel to the $x$x axis.  It's like the quadratic has been flipped upside down.

Shows the reflection of 

$y=x^2$y=x2 to $y=-x^2$y=−x2

Shows the reflection of 

$y=\left(x-1\right)\left(x+2\right)$y=(x−1)(x+2) to $y=-\left(x-1\right)\left(x+2\right)$y=−(x−1)(x+2)

$y=ax^2$y=ax2

 

This is a quadratic that has been dilated vertically by a factor of $a$a  

If $\left|a\right|>1$|a|>1 then the graph is steeper than $y=x^2$y=x2

If  $\left|a\right|<1$|a|<1 then the graph is flatter than $y=x^2$y=x2. 

Dilation of $y=x^2$y=x2 to $y=3x^2$y=3x2 and $y=\frac{1}{2}x^2$y=12 x2

$y=ax^2+k$y=ax2+k

In the graph $y=ax^2+k$y=ax2+k, the quadratic has been vertically translated by $k$k units.  

If $k>0$k>0 then the translation is up.

If $k<0$k<0 then the translation is down.

Vertical translation.  

Showing one curve $y=2x^2+5$y=2x2+5 having a vertical translation of up $5$5 units, and

another $y=2x^2-3$y=2x2−3 having a vertical translation of down $3$3 units.

$y=\left(x-h\right)^2$y=(x−h)2

The $h$h indicates the horizontal translation.  

If $h>0$h>0, that is the factor in the parentheses is $\left(x-h\right)$(x−h) than we have a horizontal translation of $h$h units right.

If $h<0$h<0 , that is the factor in the parentheses is $\left(x--h\right)=\left(x+h\right)$(x−−h)=(x+h) than we have a horizontal translations of $h$h units left.  

The graph $y=x^2$y=x2 being horizontally translated $2$2 units left

to $y=\left(x+2\right)^2$y=(x+2)2 and $1$1 unit right to $y=\left(x-1\right)^2$y=(x−1)2

Source: https://mathspace.co